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texto impreso
A congruence of lines is a (n?1)-dimensional family of lines in Pn (over C), i.e. a variety Y of dimension (and hence of codimension) n ? 1 in the Grassmannian Gr(1, Pn). A fundamental curve for Y is a curve C Pn which meets all the lines of Y [...]texto impreso
We give the list of all possible congruences in G(1,4) of degree d less than or equal to 10 and we explicitely construct most of them.texto impreso
We introduce the different focal loci (focal points, planes and hyperplanes) of (n - 1)-dimensional families (congruences) of lines in P-n and study their invariants, geometry and the relation among them. We also study some particular congruence[...]texto impreso
Congruences of lines in P3, i.e. two-dimensional families of lines, and their focal surfaces, have been a popular object of study in classical algebraic geometry. They have been considered recently by several authors as Arrondo, Goldstein, Sols,[...]texto impreso
In this paper we study the normal bundle of the embedding of subvarieties of dimension n - 1 in the Grassmann variety of lines in P(n). Making use of some results on the geometry of the focal loci of congruences ([4] and [5]), we give some crite[...]texto impreso
We give the list of all possible smooth congruences in G(1,n) which have a quadric bundle structure over a curve and we explicitely construct most of them.
